So that's one positive ABX result traced to faulty/poor equipment. I just need to convince MLXXX to look in the same direction, and we might get a sane conclusion to this discussion.

Just for the record, I find this type of wording mildly offensive, despite the habitual 'Cheers' tag.

QUOTE (MLXXX @ May 19 2008, 21:06)

[Will upload my sample clip if possible within the next 24 hours.]

There is an unresolved issue over whether the particular audio clip would meet Forum guidelines. It may be that I will be unable to upload the extract as a test clip. In that case, I guess I'll have to try to find another one that at least prima facie sounds different at 48KHz rather than 96KHz. If it can be established the difference is simply due to deficiencies in the playback chain then so be it. However that might still be a significant result if playback equipment generally available cannot play back well at 48KHz, despite theory indicating 48KHz should be sufficient.

However that might still be a significant result if playback equipment generally available cannot play back well at 48KHz, despite theory indicating 48KHz should be sufficient.

A more likely conclusion is that the equipment works fine at 48kHz, and adds additional distortion when playing material with content above 20kHz. While it would be difficult to rate which one works "better", good recordings of the sounds as played will answer the question of which is more accurate. It wouldn't surprise me if the 48kHz version were more accurate.

I do get suspicious when I look at a digital mixdown of 19KHz and 20Khz sinewaves that were created at 44.1KHz. There are so few sample points and yet as you say cooledit manages to create a realistic graphical interpolation (with this relatively simple waveform).

In contrast, when I look at 19KHz and 20KHz sinewaves created at 96KHz and mixed digitally in cooledit, there are so many more sample points in the mixdown that sophisticated interpolation would not be necessary

Sounds like you still think that downmixing makes reconstruction somewhat harder. As 2B already pointed out all of the following operations are linear:(1) sampling(2) mixing(3) reconstructionIt follows that

So? Relevance? Seriously. Grab a good DSP book that explains sampling and reconstruction. All what's been said here has been said many many times before.

QUOTE

This thread started with the downsampling to 44.1KHz question. But if downsampling to even 48KHz is a probem, 44.1KHz would be even more so.

There's no problem with downsampling to 44.1 kHz or 48 kHz (in theory). Reconstruction is also not a problem (in theory). There are simply soundcards out there that manage to screw up reconstruction. That's about it.

SebastianG, thanks for taking the time to restate this, with precision. However to me it was a side issue. I only mentioned it in response to a post of Martel's [#64]. I may at some stage in my life try to immerse myself in the mathematics that you and others obviously understand so well.

At this point I would like to cut to the chase and ascertain whether there exists a section of a recording of music that people claim is impaired when downsampled to even 48KHz.

If no-one can provide such a clip, and if theory explains why this is so, then I can rest easy when purchasing material that is at 48KHz rather than 96KHz. And I could make my own recordings of musical performances with confidence at only 48KHz.

At this point I would like to cut to the chase and ascertain whether there exists a section of a recording of music that people claim is impaired when downsampled to even 48KHz.

If no-one can provide such a clip, and if theory explains why this is so, then I can rest easy when purchasing material that is at 48KHz rather than 96KHz. And I could make my own recordings of musical performances with confidence at only 48KHz.

By "impaired" you probably meant "perceptually different".

I can't think of any reason why it should be perceptually different given a good reconstruction of both versions (48kHz versus 96kHz) simply because our human ears don't pick up ultrasonics -- at least to the best of our knowledge. This is fairly easy to test with pure tones (sine oscillator). But when people try to verify this with "normal music" instead possible reconstruction errors (aliasing or nonlinear distortions which lead to intermodulation) might make ultrasonic frequencies indirectly audible by polluting the audible spectrum. So, it's very likely that when people succeed in ABXing 48kHz versus 96kHz that something's wrong with the whole reconstruction process (from digital to air pressure). Then, the reconstructed 48kHz version could be even closer to the "original" in terms of perception.

So that's one positive ABX result traced to faulty/poor equipment. I just need to convince MLXXX to look in the same direction, and we might get a sane conclusion to this discussion.

Just for the record, I find this type of wording mildly offensive, despite the habitual 'Cheers' tag.

MLXXX, there have been posts where I have been too harsh with you. I apologise. Please let me try to explain where I am coming from, and where my frustration at this discussion comes from!

A lot of people over the years have arrived at Hydrogenaudio, stated they have almost no knowledge or understanding of the subject, yet they feel sure that they have discovered some problem with some aspect of audio that has been missed by the entire audio industry.

The icing on the cake is that the "problem" is probably due to faulty hardware or software, but rather than investigating this possibility to rule it in or out, they prefer to embark on a discussion which implies "every mathematician and engineer who ever proved how this works was an idiot" or more simply "Nyquist was wrong", while saying they have no interest in acquiring the knowledge and understanding that they lack.

That's the offensive part - the "I know nothing about this, but I'm sure all these engineers and mathematicians were wrong". The people probably don't know enough about it to realise that's what they're implying - but that's exactly what they're implying. That's what's offensive - "engineering, science, maths, theory - pah - load of junk - the output of my Creative soundcard proves it's all wrong!". Actually, stated like that, it's not offensive, just funny.

You can find such threads in the FAQ; I hoped you'd see the parallels between them, and your own.

The thing that worries me the most is the kind of rubbish that plagues boards like Audio Asylum, where any problems that might exist in audio will never be solved because there's no acceptance of the basic science behind it. I really don't want to see that kind of thing at Hydrogenaudio.

@MLXXX: You seem to want someone to prove to you that there is never a problem when downsampling 96 kHz to 48 kHz/44.1 kHz, but such a thing cannot be proven. It is only possible to prove that something does exist, not that it doesn't exist.

However, consider this. You have come to the HydrogenAudio forum, the place where all of the top experts in the field post regularly. The combined experience of these folks is hundreds if not thousands of years. So far nobody has come forward to say that they know of a case where downsampling resulted in an audible difference where it was not eventually shown to be a hardware problem. Can't you accept this as sufficient evidence that your worries are not justified?

2B, yes I can understand that some of my posts may have irritated you and others for the reason that they may have created the impression that I thought that sophisticated mathemathics can readily be disproven with some simple tests in a domestic environment with unsophisticated equipment. That is not where I am coming from.

I do not for a moment question classic Nyquist Shannon concepts. However it is not readily apparent to me how those concepts apply precisely to the human listening experience. It seems to be accepted that the upper frequency continuous sinewave response limit of the human ear (up to about 20KHz) is the relevant bandwidth limit. I have to accept on blind faith that that is all that is relevant and sufficient for the human listening experience.

I've recently spent many hours reading quite a few threads on the sampling rate topic and I would have to say the HA threads are way above the average standard for myself as a reader with an interest in the science (even if I do not fully understand it) as well as broader subjective comments.

Significantly, in no threads have I seen any upload of a file with a higher sample rate such as 96KHz claimed to be reduced in perceptible quality if played back after downsampling to a lower rate such as 48Khz.

That seems extraordinary to me. If 96KHz can sound better as is claimed in so many threads, where is the concrete illustration of the claim???

The absence of such uploads to me significantly weakens the credibility of those who claim superiority of 96KHz per se. [I exclude matters such as the fact that certain DSP operations may be more easily and accurately implemented with some software at 96KHz, e.g. a graphic equalizer function.]

QUOTE (pdq @ May 21 2008, 21:37)

However, consider this. You have come to the HydrogenAudio forum, the place where all of the top experts in the field post regularly. The combined experience of these folks is hundreds if not thousands of years. So far nobody has come forward to say that they know of a case where downsampling resulted in an audible difference where it was not eventually shown to be a hardware problem. Can't you accept this as sufficient evidence that your worries are not justified?

I have only just read this post of yours pdq, so am adding the following as an edit.

Indeed I think this is the thing. If no-one can identify an instance where 96Khz sampled music sounds superior to 48Khz to the human ear, that really is damning for the 96KHz proponents.

2B, yes I can understand that some of my posts may have irritated you and others for the reason that they may have created the impression that I thought that sophisticated mathemathics can readily be disproven with some simple tests in a domestic environment with unsophisticated equipment. That is not where I am coming from.

I do not for a moment question classic Nyquist Shannon concepts. However it is not readily apparent to me how those concepts apply precisely to the human listening experience. It seems to be accepted that the upper frequency continuous sinewave response limit of the human ear (up to about 20KHz) is the relevant bandwidth limit. I have to accept on blind faith that that is all that is relevant and sufficient for the human listening experience.

I've recently spent many hours reading quite a few threads on the sampling rate topic and I would have to say the HA threads are way above the average standard for myself as a reader with an interest in the science (even if I do not fully understand it) as well as broader subjective comments.

Significantly, in no threads have I seen any upload of a file with a higher sample rate such as 96KHz claimed to be reduced in perceptible quality if played back after downsampling to a lower rate such as 48Khz.

That seems extraordinary to me. If 96KHz can sound better as is claimed in so many threads, where is the concrete illustration of the claim???

The absence of such uploads to me significantly weakens the credibility of those who claim superiority of 96KHz per se. [I exclude matters such as the fact that certain DSP operations may be more easily and accurately implemented with some software at 96KHz, e.g. a graphic equalizer function.]

QUOTE (pdq @ May 21 2008, 21:37)

However, consider this. You have come to the HydrogenAudio forum, the place where all of the top experts in the field post regularly. The combined experience of these folks is hundreds if not thousands of years. So far nobody has come forward to say that they know of a case where downsampling resulted in an audible difference where it was not eventually shown to be a hardware problem. Can't you accept this as sufficient evidence that your worries are not justified?

I have only just read this post of yours pdq, so am adding the following as an edit.

Indeed I think this is the thing. If no-one can identify an instance where 96Khz sampled music sounds superior to 48Khz to the human ear, that really is damning for the 96KHz proponents.

Please, let this end already... Someone might claim superiority of 96 kHz to 44,1 kHz but in reality, this is mostly NOT based upon capabilities of the format itself, only upon lame implementation of playback chain, unfounded rumors or general feeling that GREATER = BETTER. There is absolutely no guarantee that a 96 kHz equipment playing a 96 kHz material will sound better than a 44,1 kHz one. There is, perhaps, just higher probability that equipment playing a 44,1kHz content will screw something up because of poor/cheap playback chain design. So by going 96 kHz you are more likely to avoid (audible) issues caused by poor filter design.If you do not trust your hardware, please go ahead and convert everything to 96kHz using SSRC, so you may find peace having "enough" samples per signal period.

If no-one can identify an instance where 96Khz sampled music sounds superior to 48Khz to the human ear, that really is damning for the 96KHz proponents.

I applaud your persistence, especially in this forum full of sceptics. Let's continue the search for a killer sample where the difference is obvious. I would be happy to record and host some (free) samples up to 24/192 kHz. Any suggestions ?

QUOTE (pdq @ May 21 2008, 21:37)

However, consider this. You have come to the HydrogenAudio forum, the place where all of the top experts in the field post regularly. The combined experience of these folks is hundreds if not thousands of years. So far nobody has come forward to say that they know of a case where downsampling resulted in an audible difference where it was not eventually shown to be a hardware problem. Can't you accept this as sufficient evidence that your worries are not justified?

Mind you, not "all of the top experts" are HA members. I find this kind of reasoning rather deceiving and even intimidating. Can't we just encourage curious people like MLXXX to perform tests and discuss the best ways to do so ? Thousands of audio professionals are moving to hi-res audio. They could all be wrong and wasting money and bandwidth. It can also be a motivation to search for (not necessarily perceptual) reasons why they prefer hi-res audio.

It seems to be accepted that the upper frequency continuous sinewave response limit of the human ear (up to about 20KHz) is the relevant bandwidth limit. I have to accept on blind faith that that is all that is relevant and sufficient for the human listening experience.

Just one more correction and then I think we can lay this topic to rest.

The relevant bandwidth limit is not the ability to hear continuous sinewaves, unless one is in the habit of listening to high frequency sinewaves. The ability to hear high frequencies in real music, even very synthetic music, is significantly lower. Being able to hear the difference after music has been lowpassed at about 16 to 17 kHz is actually quite rare, although I think there have been some verified cases. Recently someone with admitedly very unusual hearing claimed to hear much higher, but I don't recall that this was ever verified.

Let's continue the search for a killer sample where the difference is obvious. I would be happy to record and host some (free) samples up to 24/192 kHz. Any suggestions ?

Thx for your kind remarks.

I suspect that even with a killer sample, the effect might not be all that obvious.

The only suggestion I have and it is one that would only apply where a large number of string players were available (and perhaps playing at a very high standard!) is a recording made with extended range microphone(s) of the violin section of an orchestra.*

As an easier alternative, perhaps people who have in their possession some high definition recordings [recent era; 96Khz+] might be inclined to downsample one or two tracks to 48Khz [44.1Khz could be problematic for other reasons as has been mentioned in this thread] and compare the listening experience to the original sample rate.

There was one website I encountered (Mytek Digital) which had samples of different analogue to digital converters operating at the same sampling rate (192KHz) that had apparently processed the same performance of music. The website invited visitors to compare the digital versions. I could hear differences between the ADCs (which rather surprised me), but I could not hear any differences from converting the sampling from the various ADCs down to 48Khz using Audition 3. The music genre was jazz.

___________

*In the recording I referred to in post #63, the harmony between string sections was sweeter and more fluid on my AVR at 96KHz than at 48KHz. The effect was very subtle and very possibly due to hardware issues, but of a handful of high definition recordings I have evaluated it is the only one where I found I could hear a difference. Subjectively it was similar to the difference between 24 bits and 24 bits truncated to 16 bits, i.e. a very subtle differerence to do with the smoothness of the sound.

Clearly not, but I think you'd be amazed at some of the people who are (anonymously). You can catch more of them on various mailing lists, should you want to.

QUOTE

I find this kind of reasoning rather deceiving and even intimidating. Can't we just encourage curious people like MLXXX to perform tests and discuss the best ways to do so ? Thousands of audio professionals are moving to hi-res audio. They could all be wrong and wasting money and bandwidth. It can also be a motivation to search for (not necessarily perceptual) reasons why they prefer hi-res audio.

SebastianG, thanks for taking the time to restate this, with precision. However to me it was a side issue. I only mentioned it in response to a post of Martel's [#64]. I may at some stage in my life try to immerse myself in the mathematics that you and others obviously understand so well.

At this point I would like to cut to the chase and ascertain whether there exists a section of a recording of music that people claim is impaired when downsampled to even 48KHz.

If no-one can provide such a clip, and if theory explains why this is so, then I can rest easy when purchasing material that is at 48KHz rather than 96KHz. And I could make my own recordings of musical performances with confidence at only 48KHz.

For recording, why not just split the diff and record at 88.2/24bit? That's an even multiple SR of 44.1, computationally a snap if you need to downsample to CD rate. And it's well above even the ~60kHz 'safety' rate proposed by Lavry and others for surmounting any real or theoretical problems with suboptimal antialias and anti-image filters. At 88.2 you should have no pangs of anxiety (even though I think it's way overkill).

QUOTE

I do not for a moment question classic Nyquist Shannon concepts. However it is not readily apparent to me how those concepts apply precisely to the human listening experience. It seems to be accepted that the upper frequency continuous sinewave response limit of the human ear (up to about 20KHz) is the relevant bandwidth limit. I have to accept on blind faith that that is all that is relevant and sufficient for the human listening experience.

First, my impression is that understanding the maths behind DSP is really the only way to *truly* understand what's going on (which I do not claim I do). As you see some aspects of DSP really are counterintuitive on their face....like the 'few samples at high frequencies' thing.

Second, every attempt so far to argue for the physiological need for higher sample rates in order to produce realistic audio, founders at the blind test stage. Thus proponents have to resort to arguments like: it's a hypersonic effect that is only detectable by brain imaging! (though the 'effect curiously seems to last much longer than the stimulus, and requires custom made playback gear) or, some musical instruments have lots of energy above 20kHz! (and some visible light sources have lots of energy in the UV or infrared ranges...so?) or , what about bone conduction?! (what about it? it's a vibration effect that requires the source to be very close to the body). The only argument with any solid foundation is: 44.1 puts the onus on engineers to make their brickwall filters very good indeed, or to use oversampling, because at 44.1 the cutoff frequency (22.05) is so close to the audible limit. So shoddy implementation at recording or playback could lead to audible artifacts.

You don't have to accept on 'blind faith' that the ear's passband for sounds transmitted through air extends 'only' up to the mid-20's at very best, these numbers weren't pulled from thin air, there is a scientific literature on psychoacoustics and the physiology of audition dating back a century.

QUOTE

The absence of such uploads to me significantly weakens the credibility of those who claim superiority of 96KHz per se

Well, no kidding! I don't know where you get the impression that '96 kHz per se is superior' is the consensus on HA.org. I'd say it's quite the opposite. Of course, once we travel beyond the confines of 'the village' here, and out into the woods of other 'audiophile' forums, then we start to see claims that have more foundation in belief than evidence.

Let's continue the search for a killer sample where the difference is obvious. I would be happy to record and host some (free) samples up to 24/192 kHz. Any suggestions ?

Thx for your kind remarks.

As an easier alternative, perhaps people who have in their possession some high definition recordings [recent era; 96Khz+] might be inclined to downsample one or two tracks to 48Khz [44.1Khz could be problematic for other reasons as has been mentioned in this thread] and compare the listening experience to the original sample rate.[/size]

Here is a site that claims to offer the same sample recorded in 96/24 and 44/16.

You don't have to accept on 'blind faith' that the ear's passband for sounds transmitted through air extends 'only' up to the mid-20's at very best, these numbers weren't pulled from thin air, there is a scientific literature on psychoacoustics and the physiology of audition dating back a century.

Thx for your various comments krabapple. On this particular aspect, the point I was trying to make is that although it can be said based on decades of testing that the human ear has a bandwidth of around 20KHz when tested with continuous tones, I am obliged to accept on blind faith that that is all that is required as the bandwidth of a digital reconstruction process.

To many people, the two bandwidths are equivalent and no further analysis is necessary.

I am hesitant as real life audio sources can start and stop abruptly and asynchronously. We have a perception of the direction of a sound source as well as its pitch and tonal quality. All of this strikes me as very complex. It is not clear to me (but has to be accepted with blind faith) that because our ears can only hear a continuous tone up to about 20KHz, a bandwidth of 20KHz in the electronics is sufficient for recording and reproducing music.

Don't you think that it is futile to try to force a point home without backing it up with the necessary objective testing data as well as some semblance of knowledge of the mathematics behind longitudinal waveforms and the human ear's response to them?

You don't have to accept on 'blind faith' that the ear's passband for sounds transmitted through air extends 'only' up to the mid-20's at very best, these numbers weren't pulled from thin air, there is a scientific literature on psychoacoustics and the physiology of audition dating back a century.

Thx for your various comments krabapple. On this particular aspect, the point I was trying to make is that although it can be said based on decades of testing that the human ear has a bandwidth of around 20KHz when tested with continuous tones, I am obliged to accept on blind faith that that is all that is required as the bandwidth of a digital reconstruction process.

To many people, the two bandwidths are equivalent and no further analysis is necessary.

Well, if anything, 'test tones" can be *more* useful for discriminating differnces, than complex samples like music, where psychoacoustic masking effects kick in.

QUOTE

I am hesitant as real life audio sources can start and stop abruptly and asynchronously. We have a perception of the direction of a sound source as well as its pitch and tonal quality. All of this strikes me as very complex. It is not clear to me (but has to be accepted with blind faith) that because our ears can only hear a continuous tone up to about 20KHz, a bandwidth of 20KHz in the electronics is sufficient for recording and reproducing music.

Again, the documented upper limit of hearing is more like 24, not 20, kHz, but this is for children and exceptional adults. Typically adult hearing's increasingly degraded from 16 kHz on up, and even at best in our youth, we are always more sensitive to some ranges than others. That's the way our hearing works, and it makes good evolutionary sense for us to be more sensitive to midrange (speech, vocalization) than to what bats hear. By contrast, the delivered response of CD audio is essentially *flat* to about 20.

The 'it strikes me as complex' is close to an argument from personal incredulity. and the answer is: more reading about how digital audio *works*. The argument about transients ('abrupt starts and stops'), phase ('asynchonicity') and directionality have been done to death and tend to devolve back to one side refusing to accept the science and the maths 'on faith' , though they haven't really grasped the science and the maths in the first place.

Thx for your various comments krabapple. On this particular aspect, the point I was trying to make is that although it can be said based on decades of testing that the human ear has a bandwidth of around 20KHz when tested with continuous tones, I am obliged to accept on blind faith that that is all that is required as the bandwidth of a digital reconstruction process.

To many people, the two bandwidths are equivalent and no further analysis is necessary.

I am hesitant as real life audio sources can start and stop abruptly and asynchronously. We have a perception of the direction of a sound source as well as its pitch and tonal quality. All of this strikes me as very complex. It is not clear to me (but has to be accepted with blind faith) that because our ears can only hear a continuous tone up to about 20KHz, a bandwidth of 20KHz in the electronics is sufficient for recording and reproducing music.

You're doing it again - you're assuming that, in the entire history of psychoacoustics, no one tried low pass filtering impulses to check the limit that way; no one tried manipulating interaural level, time, and frequency to determine the effects; and no one tried recording audio at high bandwidth, and checked for the audibility of various low pass filters.

krabapple put it succinctly...

QUOTE

The 'it strikes me as complex' is close to an argument from personal incredulity. and the answer is: more reading about how digital audio *works*.

However that might still be a significant result if playback equipment generally available cannot play back well at 48KHz, despite theory indicating 48KHz should be sufficient.

A more likely conclusion is that the equipment works fine at 48kHz, and adds additional distortion when playing material with content above 20kHz. While it would be difficult to rate which one works "better", good recordings of the sounds as played will answer the question of which is more accurate. It wouldn't surprise me if the 48kHz version were more accurate.

Thanks Cabbagerat. It seems that even if a particular file did seem to sound better when played at one sample rate than another, using a particular playback chain, there could be any number of possible reasons for that outcome.

QUOTE (2Bdecided @ May 22 2008, 20:49)

You're doing it again - you're assuming that, in the entire history of psychoacoustics, no one tried low pass filtering impulses to check the limit that way; no one tried manipulating interaural level, time, and frequency to determine the effects; and no one tried recording audio at high bandwidth, and checked for the audibility of various low pass filters.

2B, I have for years assumed such tests would have been done.

_____________________

Perhaps this thread has reached a natural end, unless there are any actual audio clips at around 96KHz or more that have been identified (and can be linked to, or uploaded ) that appear to sound better at the higher sampling rate than when downsampled to 48Khz. Though if anyone has the courage to identify such a clip, they should be ready for their claim to be challenged!

Perhaps this thread has reached a natural end, unless there are any actual audio clips at around 96KHz or more that have been identified (and can be linked to, or uploaded ) that appear to sound better at the higher sampling rate than when downsampled to 48Khz. Though if anyone has the courage to identify such a clip, they should be ready for their claim to be challenged!

Man, this is not about courage, this would be about breaking the human body limits! And, please, rule out the sampling rate from your considerations, a 96kHz waveform lowpassed at 24 kHz bears exactly the same information as the same waveform downsampled to 48 kHz (if downsampled ideally).If I were you, I would first "investigate" the possibility of identifying a 24 kHz lowpass filter. Try and start a new thread.

When file 1 and file 3 were attempted to be ABXd a problem arose as the tweeter in trying to handle the 24999Hz tone was not able to reproduce the 8333Hz at full amplitude.

[With a microphone at 1m from the tweeter and using an oscilliscope connected to the output of the analogue mixer, the peak to peak voltage was slightly less when playing file 3 compared with file 1. The waveform shape was different as well.]

After temporarily reducing the amplitude of file 1 by a small amount, the files still sounded different when an ABX was attempted.

However I was concerned that the tweeter might be creating spurious effects, so I changed the experimental setup.

2nd test:Stereo file A created with file 1 (8333Hz) as the left channel and file 2 (24999Hz) as the right channel. Stereo file B created with file 1 (8333Hz) as the left channel and zero signal for the right channel.

Playback volume of the left speaker was tested with the microphone 1 metre in front of the tweeter and feeding the oscilloscope. Amplitude of the waveform from the left speaker remained constant whether or not the right channel was playing, i.e. whether file A or file B was played.

At a reasonable listening distance, A and B sounded different (file A seemed louder and a little richer).

I was concerned that the separation of the speakers was so great it was creating a sound field full of peaks and troughs. The wavelength of 8333Hz is only a little over 4 centimetres.

3rd test:In the interest of science, I moved the front left and front right home theatre speaker enclosures so their sides were touching, and played files A and B in an endless loop.

Even at a distance of 8 meters on axis from the speakers there were very noticeable nodes in the sound field. As in test 2, file A seemed louder and little richer. This was clearcut. (However it was important not to move as the loop played.)

As a type of control, I created a file 3L, which had the contents of file 3 in the right channel, and nothing in the left channel. When this was played, the sound field was full of nodes. This was to be expected. Our living room is not an anechoic chamber.

Also, with the speakers adjacent, I positioned the microphone about 1.5 metres away and observed the oscilloscope. The waveform was not perfect but it was very different to a sine wave when one speaker was reproducing the 8333Hz tone and the other the 3rd harmonic.

Conclusions:

Although the third harmonic of a tone at 8333Hz cannot be heard when played by itself (i.e. as a tone of 24999Hz) by adult human beings, it can have an impact on the human listening experience, when the fundamental frequency is also being reproduced by a loudspeaker system in a home environment.

If the 24999Hz tone is absent, the listening experience can be different. Subjectively (for me) it is slightly less rich. Also I found that when the harmonic was present, I perceived the pitch as sounding slighter sharper if my ears were fresh, but flatter if I had been ABXing for a while. [This certainly didn't assist the ABX process!]

The effect was subtle.

Some audio cannot be downsampled to 44.1KHz, or even 48KHz, without affecting the perceived sound.

As it is late, I will not attempt to upload any of the test files. They are quite easy to generate using cooledit or audition, anyway. [Edit: Stereo test files are now at post #105.]

I imagine that these results are no surprise to many readers, but will surprise some others.

How this type of experiment relates to the proposition that an audio bandwidth of around 20KHz is sufficient for the human listening experience I will leave to others to comment on, if they so wish.

I note that by sending the third harmonic through a separate amplifier, I avoided the issue of intermodulation distortion in the amplifier and the speakers [though not any possible IMD in my own hearing]. I listened at what I'd term a 'moderate' level, certainly not a loud level for listening to music. The 24999Hz waveform when displayed on the oscilloscope looked quite smooth (a sinusoid) when only it was being played. Similarly when only the 8333Hz waveform was played, there was a smooth sinusoid. However when the combined waveform was played through one speaker [or when played with two adjacent speakers each taking a separate frequency], the shape of the waveform altered on the oscilliscope, and the quality of the sound changed slightly for my ears.